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A note on the cut-elimination proof in "truth without contra(di)ction"

Fjellstad, Andreas
Peer reviewed, Journal article
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URI
https://hdl.handle.net/1956/22044
Date
2020
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Original version
The Review of Symbolic Logic. 2020, 13 (4), 882-886.   https://doi.org/10.1017/s1755020319000571
Abstract
This note shows that the permutation instructions presented by Zardini in "Truth without contra(di)ction" (RSL, 2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the non-contractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counter-example is of the kind that leaves open the question whether cut can be shown to be eliminable in the sequent calculus for IKTω with an alternative strategy.
Publisher
Cambridge University Press
Journal
The Review of Symbolic Logic
Copyright
Copyright Association for Symbolic Logic, 2019

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